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Understanding the data and reaching accurate conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have been widely used for this purpose in various fields. One critically important yet less explored aspect is capturing and analyzing uncertainties in the data and model. Proper quantification of uncertainty helps to provide valuable information to obtain accurate diagnosis. This paper reviewed related studies conducted in the last 30 years (from 1991 to 2020) in handling uncertainties in medical data using probability theory and machine learning techniques. Medical data is more prone to uncertainty due to the presence of noise in the data. So, it is very important to have clean medical data without any noise to get accurate diagnosis. The sources of noise in the medical data need to be known to address this issue. Based on the medical data obtained by the physician, diagnosis of disease, and treatment plan are prescribed. Hence, the uncertainty is growing in healthcare and there is limited knowledge to address these problems. Our findings indicate that there are few challenges to be addressed in handling the uncertainty in medical raw data and new models. In this work, we have summarized various methods employed to overcome this problem. Nowadays, various novel deep learning techniques have been proposed to deal with such uncertainties and improve the performance in decision making. [ABSTRACT FROM AUTHOR]

Payment cards offer a simple and convenient method for making purchases. Owing to the increase in the usage of payment cards, especially in online purchases, fraud cases are on the rise. The rise creates financial risk and uncertainty, as in the commercial sector, it incurs billions of losses each year. However, real transaction records that can facilitate the development of effective predictive models for fraud detection are difficult to obtain, mainly because of issues related to confidentially of customer information. In this paper, we apply a total of 13 statistical and machine learning models for payment card fraud detection using both publicly available and real transaction records. The results from both original features and aggregated features are analyzed and compared. A statistical hypothesis test is conducted to evaluate whether the aggregated features identified by a genetic algorithm can offer a better discriminative power, as compared with the original features, in fraud detection. The outcomes positively ascertain the effectiveness of using aggregated features for undertaking real-world payment card fraud detection problems. [ABSTRACT FROM AUTHOR]

This paper addresses the general problem of designing ordinal classification methods based on comparing actions with limiting boundaries of ordered classes (categories). The fundamental requirement of the method consists of setting a relational system (D,S), where S and D are reflexive and transitive relations, respectively, S should be compatible with the order of the set of classes, and D is a subset of S. An asymmetric preference relation P is defined from S. Other requirements are imposed on the actions which compose the limiting boundaries between adjacent classes, in such a way that each class is closed below and above. The paper proposes S-based and P-based assignment procedures. Each of them is composed of two complementary assignment procedures, which correspond through the transposition operation and should be used conjointly. The methods work under several basic conditions on the set of limiting boundaries. Under other more demanding separability requirements, each procedure fulfills the set of structural properties established for other outranking-based ordinal classification methods. Our proposal avoids the conflict between the required correspondence through the transposition operation and the assignment of limiting actions to the classes to which they belong. We thus propose very diverse S and P-based ordinal classification approaches with desirable properties, which can be designed by using decision models with the capacity to build preference relations fulfilling the basic requirements to S and D. [ABSTRACT FROM AUTHOR]

Gastric Cancer is the most common malignancy of the digestive tract, which is the third leading cause of cancer-related mortality worldwide. The early prognosis methods, especially Machine Learning (ML)-based approaches are one of the main strategies against GC, which have become a necessity to identify and prognosticate the factors that affect the GC. They enable the specialists to accelerate the subsequent clinical management of patients, who suffer from the GC. This paper aims at creating an Ensemble Method inspired from ML to predict the most significant factors of the GC occurrence. The main objective of this research is to predict the probabilities of the GC occurrence and its associated deaths. To achieve this goal, the created EM benefits from some ML-based methods, including Least Absolute Shrinkage and Selection Operator (LASSO)/Ridge Regression, Elastic Net, Logistic Regression (LR), Random Forest (RF), Gradient Boosting Decision Trees (GBDTs), and Deep Neural Network (DNN). The purpose of the provided EM is to lessen the prediction errors for the large number of the patients' features. The main novelties of this research include: (i) A sequential EM created by a Stacking method to predict the probability of the GC and associated deaths; (ii) Benefiting from the significance level to make an accurate prediction; (iii) Employing two Chi-square tests to select the influent features; (iv) Tuning the parameters of the applied ML models to avoid over-fitting and intensifying the errors; (v) Applying different kinds of the regression methods to treat hyper-dimension cases; (vi) A new model for weighting the applied ML models. The outcomes of the implementation of the created EM in seven pioneer hospitals in the field of GC show that the designed EM generates more precise predictions with an accuracy of 97.9% and 76.3% to predict the GC and its associated deaths, respectively. Moreover, the obtained results from the Area Under Curve (AUC) validates and confirms the capability of the created EM to predict the probability of the GC and its related deaths with an accuracy of 98% and 90% to predict the GC and its associated deaths, respectively. [ABSTRACT FROM AUTHOR]

In recent decades, breast cancer has become one of the leading causes of mortality among women. This disease is not preventable because of its unknown causes; however, its early diagnosis increases patients' recovery chances. Machine learning (ML) can be utilized to improve treatment outcomes in healthcare operations while diminishing costs and time. In this research, we suggest two novel feature selection (FS) methods based upon an imperialist competitive algorithm (ICA) and a bat algorithm (BA) and their combination with ML algorithms. This study aims to enhance diagnostic models' efficiency and present a comprehensive analysis to help clinical physicians make more precise and reliable decisions. K-nearest neighbors (KNN), support vector machine (SVM), decision tree (DT), Naive Bayes, AdaBoost (AB), linear discriminant analysis (LDA), random forest (RF), logistic regression (LR), and artificial neural network (ANN) are some of the methods employed. Sensitivity, accuracy, precision, mean absolute error F-score, root mean square error, Kappa, and relative absolute error calculated the performance of the methods. This paper applied a distinctive integration of evaluation measures and ML algorithms using the wrapper feature selection based on ICA (WFSIC) and BA (WFSB) separately. We compared two proposed approaches for the performance of the classifiers. Also, we compared our best diagnostic model with previous works reported in the literature survey. Experimentations were performed on the Wisconsin diagnostic breast cancer (WDBC) dataset. Results reveal that the proposed framework that uses the BA with an accuracy of 99.12% surpasses the framework using the ICA and most previous works. Additionally, the RF classifier in the approach of FS based on BA emerges as the best model and outperforms others regarding its criteria. Besides, the results illustrate the role of our techniques in reducing the dataset dimensions up to 90% and increasing the performance of diagnostic models by over 99%. Moreover, the result demonstrates that there are more critical features than the optimum dataset obtained by proposed FS approaches that have been selected by most ML models, including the standard error of area, concavity, smoothness, perimeter, the worst of texture, compactness, radius, symmetry, smoothness, concavity, and the mean of concave points, fractal dimension, compactness, concavity that can remarkably affect the efficiency of breast cancer prediction. This study illustrates the role of our approaches in enhancing treatment outcomes in healthcare operations. [ABSTRACT FROM AUTHOR]

The paper investigates hyperparameter optimization problem. Hyperparameters are the parameters of model parameter distribution. The adequate choice of hyperparameter values prevents model overfit and allows it to obtain higher predictive performance. Neural network models with large amount of hyperparameters are analyzed. The hyperparameter optimization for models is computationally expensive. The paper proposes modifications of various gradient-based methods to simultaneously optimize many hyperparameters. The paper compares the experiment results with the random search. The main impact of the paper is hyperparameter optimization algorithms analysis for the models with high amount of parameters. To select precise and stable models the authors suggest to use two model selection criteria: cross-validation and evidence lower bound. The experiments show that the models optimized using the evidence lower bound give higher error rate than the models obtained using cross-validation. These models also show greater stability when data is noisy. The evidence lower bound usage is preferable when the model tends to overfit or when the cross-validation is computationally expensive. The algorithms are evaluated on regression and classification datasets. [ABSTRACT FROM AUTHOR]

Portfolio selection is recognized as the birth-place of modern finance; Markowitz emphasizes computing whole efficient frontiers. Moreover, computing efficient sets has long been a topic in multiple-objective optimization. After portfolio selection, an important research direction is capital asset pricing models (CAPM). Black and Fama prove the existence of a unique zero-covariance portfolio on the minimum-variance frontier. By the zero-covariance relationship, Roll then classifies the minimum-variance frontier into a positive-covariance side and a negative-covariance side; Fama and Roll further prove zero-covariance CAPM. Recently, researchers gradually realize additional criteria and extend portfolio selection into multiple-objective portfolio selection. Consequently, the minimum-variance frontier extends to a minimum-variance surface. Moreover, the extension naturally raises questions of classifying the surface for multiple-objective CAPM. There has been no such research until now. In such an area, this paper contributes to the literature by extending the classification. We classify the surface into a positive-covariance side and a negative-covariance side, although the classification depends on specific portfolios and is thus non-uniform. We then analyze classification properties and extend relevant theorems by proposing conjectures, although the conjectures are disproved by theorems and counter-examples. Moreover, we forward the research methodology to general k-objective models, so research arenas for multiple-objective CAPM are opened. This paper brings researchers one step closer to classifying the minimum-variance surface and extending CAPM. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to propose two new procedures that deal with overfitting problem using neural techniques for variable selection and business failure prediction. The first procedure, called HVS-AUC, is based simultaneously on (i) the backward search, (ii) the HVS measure (Heuristic for Variable Selection), and (iii) the AUC criterion (Area Under Curve). The second procedure, called forward-AUC, is based on (i) the forward search and (ii) the AUC criterion. Using a sample of bankrupt and non-bankrupt firms in France, the implementation of the procedures using neural networks shows that the profitability, the repayment capacity, the taxation, and the importance of investment have a strong explanatory power in bankruptcy prediction. These procedures also provide more parsimonious and more efficient models compared to Linear Discriminant Analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a regression-based approach for obtaining a set of weights for multi-criteria ABC inventory analysis, which differ across classification criteria but are common across inventory items and follow a predetermined descending ordering scheme regarding the relative importance of classification criteria. The proposed alternative is based on the Inequality Constrained Least Squared model and is to be compared with the existing linear and non-linear programming models available in the literature. [ABSTRACT FROM AUTHOR]

One-Class Classification (OCC) is a supervised learning technique for classification whereby the classifier is obtained only by training the objects from the target class and identifying whether new observations belong to the class or not. In this paper, we propose a novel approach to OCC, which is based on optimal covering of the target objects by 'good' norm balls. The proposed classifier consists of the selected norm balls from an integer programming model where the finite norm ball candidates from the target objects are used. Computational experiments were carried out to examine the performance and characteristics of the proposed classifier using artificial and real data from the UCI Repository. The results showed that the proposed model was comparable to existing OCC methods in the comparison group. In addition, the proposed model demonstrated high sparsity leading to low testing burden and robustness to noises. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TWSVM) and twin support vector regression (TSVR) are newly emerging efficient machine learning techniques which offer promising solutions for classification and regression challenges respectively. TWSVM is based upon the idea to identify two nonparallel hyperplanes which classify the data points to their respective classes. It requires to solve two small sized quadratic programming problems (QPPs) in lieu of solving single large size QPP in support vector machine (SVM) while TSVR is formulated on the lines of TWSVM and requires to solve two SVM kind problems. Although there has been good research progress on these techniques; there is limited literature on the comparison of different variants of TSVR. Thus, this review presents a rigorous analysis of recent research in TWSVM and TSVR simultaneously mentioning their limitations and advantages. To begin with, we first introduce the basic theory of support vector machine, TWSVM and then focus on the various improvements and applications of TWSVM, and then we introduce TSVR and its various enhancements. Finally, we suggest future research and development prospects. [ABSTRACT FROM AUTHOR]

The training phase is the most crucial stage during the machine learning process. In the case of labeled data and supervised learning, machine learning entails minimizing the loss function under various constraints. We provide an innovative model for learning with numerous data sets, resulting from the application of multicriteria optimization techniques to existing deep learning algorithms. Data fitting is formulated as a multicriteria model in which each criterion measures the data fitting error on a specific data set. This is an optimization model involving a vector-valued function, and it has to be analyzed using the notion of Pareto efficiency. We present stability results for efficient solutions in the presence of input and output data perturbations. The multiple data set environment comes into play to eliminate the bias caused by the selection of a specific training set. To apply this concept, we present a scalarization strategy as well as numerical experiments in digit classification using MNIST data. [ABSTRACT FROM AUTHOR]

Supervised classification is one of the most powerful techniques to analyze data, when a-priori information is available on the membership of data samples to classes. Since the labeling process can be both expensive and time-consuming, it is interesting to investigate semi-supervised algorithms that can produce classification models taking advantage of unlabeled samples. In this paper we propose LapReGEC, a novel technique that introduces a Laplacian regularization term in a generalized eigenvalue classifier. As a result, we produce models that are both accurate and parsimonious in terms of needed labeled data. We empirically prove that the obtained classifier well compares with other techniques, using as little as 5% of labeled points to compute the models. [ABSTRACT FROM AUTHOR]

One effective technique that has recently been considered for solving classification problems is parametric ν -support vector regression. This method obtains a concurrent learning framework for both margin determination and function approximation and leads to a convex quadratic programming problem. In this paper we introduce a new idea that converts this problem into an unconstrained convex problem. Moreover, we propose an extension of Newton's method for solving the unconstrained convex problem. We compare the accuracy and efficiency of our method with support vector machines and parametric ν -support vector regression methods. Experimental results on several UCI benchmark data sets indicate the high efficiency and accuracy of this method. [ABSTRACT FROM AUTHOR]

Many problems in operations research can be solved by combinatorial optimization. Fixed-length subset selection is a family of combinatorial optimization problems that involve selection of a set of unique objects from a larger superset. Feature selection, p-median problem, and column subset selection problem are three examples of hard problems that involve search for fixed-length subsets. Due to their high complexity, exact algorithms are often infeasible to solve real-world instances of these problems and approximate methods based on various heuristic and metaheuristic (e.g. nature-inspired) approaches are often employed. Selecting column subsets from massive data matrices is an important technique useful for construction of compressed representations and low rank approximations of high-dimensional data. Search for an optimal subset of exactly k columns of a matrix, Am×n, k, is a well-known hard optimization problem with practical implications for data processing and mining. It can be used for unsupervised feature selection, dimensionality reduction, data visualization, and so on. A compressed representation of raw real-world data can contribute, for example, to reduction of algorithm training times in supervised learning, to elimination of overfitting in classification and regression, to facilitation of better data understanding, and to many other benefits. This paper proposes a novel genetic algorithm for the column subset selection problem and evaluates it in a series of computational experiments with image classification. The evaluation shows that the proposed modifications improve the results obtained by artificial evolution. [ABSTRACT FROM AUTHOR]

Traditional control charts assume a baseline parametric model, against which new observations are compared in order to identify significant departures from the baseline model. To monitor a process without a baseline model, real-time contrasts (RTC) control charts were recently proposed to monitor classification errors when seperarting new observations from limited phase I data using a binary classifier. In contrast to the RTC framework, the distance between an in-control dataset and a dataset of new observations can also be used to measure the shift of the process. In this paper, we propose a distance-based multivariate process control chart using support vector machines (SVM), referred to as D-SVM chart. The SVM classifier provides a continuous score or distance from the boundary for each observation and allows smaller sample sizes than the previously random forest based RTC charts. An extensive experimental study shows that the RTC charts with the SVM scores are more efficient than those with the random forest for detecting changes in high-dimensional processes and/or non-normal processes. A real-life example from a mobile phone assembly process is also considered. [ABSTRACT FROM AUTHOR]

The two-group classification problem consists in constructing a classifier that can distinguish between the two groups. In this paper, we consider the two-group classification problem which consists in determining a hyperplane that minimizes the number of misclassified points. We assume that the data set is numeric and with no missing data. We develop a tabu search (TS) heuristic for solving this NP-hard problem. The TS approach is based on a more convenient equivalent formulation of the classification problem. We also propose supplementary new intensification phases based on surrogate constraints. The results of the conducted computational experiments show that our TS algorithms produce solutions very close to the optimum and require significantly lower computational effort, so it is a valuable alternative to the MIP approaches. Moreover the tabu search procedures showed in this paper can be extended in a natural way to the general classification problem, which consists of generating more than one separating hyperplanes. [ABSTRACT FROM AUTHOR]

Classification of imbalanced data is challenging when outliers exist. In this paper, we propose a supervised learning method to simultaneously classify imbalanced data and reduce the influence of outliers. The proposed method is a cost-sensitive extension of the relaxed support vector machines (RSVM), where the restricted penalty free-slack is split independently between the two classes in proportion to the number samples in each class with different weights, hence given the name weighted relaxed support vector machines (WRSVM). We compare classification results of WRSVM with SVM, WSVM and RSVM on public benchmark datasets with imbalanced classes and outlier noise, and show that WRSVM produces more accurate and robust classification results. [ABSTRACT FROM AUTHOR]

In this paper, we present a new general formulation for multiobjective optimization that can accommodate several interactive methods of different types (regarding various types of preference information required from the decision maker). This formulation provides a comfortable implementation framework for a general interactive system and allows the decision maker to conveniently apply several interactive methods in one solution process. In other words, the decision maker can at each iteration of the solution process choose how to give preference information to direct the interactive solution process, and the formulation enables changing the type of preferences, that is, the method used, whenever desired. The first general formulation, GLIDE, included eight interactive methods utilizing four types of preferences. Here we present an improved version where we pay special attention to the computational efficiency (especially significant for large and complex problems), by eliminating some constraints and parameters of the original formulation. To be more specific, we propose two new formulations, depending on whether the multiobjective optimization problem to be considered is differentiable or not. Some computational tests are reported showing improvements in all cases. The generality of the new improved formulations is supported by the fact that they can accommodate six interactive methods more, that is, a total of fourteen interactive methods, just by adjusting parameter values. [ABSTRACT FROM AUTHOR]

The Dempster-Shafer theory of belief functions has proved to be a powerful formalism for uncertain reasoning. However, belief functions on a finite frame of discernment Ω are usually defined in the power set 2, resulting in exponential complexity of the operations involved in this framework, such as combination rules. When Ω is linearly ordered, a usual trick is to work only with intervals, which drastically reduces the complexity of calculations. In this paper, we show that this trick can be extrapolated to frames endowed with an arbitrary lattice structure, not necessarily a linear order. This principle makes it possible to apply the Dempster-Shafer framework to very large frames such as the power set, the set of partitions, or the set of preorders of a finite set. Applications to multi-label classification, ensemble clustering and preference aggregation are demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new optimization framework for improving feature selection in medical data classification. We call this framework Support Feature Machine (SFM). The use of SFM in feature selection is to find the optimal group of features that show strong separability between two classes. The separability is measured in terms of inter-class and intra-class distances. The objective of SFM optimization model is to maximize the correctly classified data samples in the training set, whose intra-class distances are smaller than inter-class distances. This concept can be incorporated with the modified nearest neighbor rule for unbalanced data. In addition, a variation of SFM that provides the feature weights (prioritization) is also presented. The proposed SFM framework and its extensions were tested on 5 real medical datasets that are related to the diagnosis of epilepsy, breast cancer, heart disease, diabetes, and liver disorders. The classification performance of SFM is compared with those of support vector machine (SVM) classification and Logical Data Analysis (LAD), which is also an optimization-based feature selection technique. SFM gives very good classification results, yet uses far fewer features to make the decision than SVM and LAD. This result provides a very significant implication in diagnostic practice. The outcome of this study suggests that the SFM framework can be used as a quick decision-making tool in real clinical settings. [ABSTRACT FROM AUTHOR]

New challenges in knowledge extraction include interpreting and classifying data sets while simultaneously considering related information to confirm results or identify false positives. We discuss a data fusion algorithmic framework targeted at this problem. It includes separate base classifiers for each data type and a fusion method for combining the individual classifiers. The fusion method is an extension of current ensemble classification techniques and has the advantage of allowing data to remain in heterogeneous databases. In this paper, we focus on the applicability of such a framework to the protein phosphorylation prediction problem. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) has attracted considerable attentions recently due to its successful applications in various domains. However, by maximizing the margin of separation between the two classes in a binary classification problem, the SVM solutions often suffer two serious drawbacks. First, SVM separating hyperplane is usually very sensitive to training samples since it strongly depends on support vectors which are only a few points located on the wrong side of the corresponding margin boundaries. Second, the separating hyperplane is equidistant to the two classes which are considered equally important when optimizing the separating hyperplane location regardless the number of training data and their dispersions in each class. In this paper, we propose a new SVM solution, adjusted support vector machine (ASVM), based on a new loss function to adjust the SVM solution taking into account the sample sizes and dispersions of the two classes. Numerical experiments show that the ASVM outperforms conventional SVM, especially when the two classes have large differences in sample size and dispersion. [ABSTRACT FROM AUTHOR]

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed. [ABSTRACT FROM AUTHOR]

In credit card portfolio management, predicting the cardholder’s spending behavior is a key to reduce the risk of bankruptcy. Given a set of attributes for major aspects of credit cardholders and predefined classes for spending behaviors, this paper proposes a classification model by using multiple criteria linear programming to discover behavior patterns of credit cardholders. It shows a general classification model that can theoretically handle any class-size. Then, it focuses on a typical case where the cardholders’ behaviors are predefined as four classes. A dataset from a major US bank is used to demonstrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces multicriteria decision-aid methods for assigning alternatives to pre-defined categories and develops a unified framework for preference aggregation methods that are based on concordance and non-discordance principles. Within this framework, we propose new multicriteria classification procedures based on non-totally compensatory measures of preference and similarity. We assume that the categories are given a priori and are characterised by fictitious alternatives serving as reference points, each representing a typical element of a category, or each representing a boundary between two categories. Several assignment methods are presented, all based on a filtering process exploiting binary relations constructed following the concordance and non-discordance principles. We first consider the case of ordered categories and a filtering procedure exploiting valued preference relations is proposed for assessing the membership of alternatives in categories. Then we consider the case of non-ordered categories and filtering methods exploiting valued indifference relations are introduced. Finally, a small example is given. [ABSTRACT FROM AUTHOR]

Multi-criteria decision analysis (MCDA) has been increasingly adopted to solve decision-making problems involving multiple options and multiple criteria. These methods have been proven to improve the analytic rigor, transparency, and auditability of the decision-making process by integrating the performance of options in different criteria and balancing subjective preferences from different stakeholders. This review aims to map the academic research on multi-criteria sorting, classification and clustering methods, and highlights the key research trends and avenues by conducting a bibliometric analysis. We contribute to the body of knowledge in multi-criteria decision analysis in four ways: (1) identifying the most influential articles on this topic, (2) mapping the research on multi-criteria sorting, classification and clustering methods, (3) visualizing the trends in this field of research through network analysis, and (4) highlighting areas for future research. The results of this study help academics and practitioners to navigate the literature on MCDA methods, provide a map of existing evidence, and recommend promising avenues for future research. [ABSTRACT FROM AUTHOR]

A land classification method was designed for the Community of Madrid (CM), which has lands suitable for either agriculture use or natural spaces. The process started from an extensive previous CM study that contains sets of land attributes with data for 122 types and a minimum-requirements method providing a land quality classification (SQ) for each land. Borrowing some tools from Operations Research (OR) and from Decision Science, that SQ has been complemented by an additive valuation method that involves a more restricted set of 13 representative attributes analysed using Attribute Valuation Functions to obtain a quality index, QI, and by an original composite method that uses a fuzzy set procedure to obtain a combined quality index, CQI, that contains relevant information from both the SQ and the QI methods. [ABSTRACT FROM AUTHOR]

Uncertainty in data occurs in diverse applications due to measurement errors, data incompleteness, and multiple repeated measurements. Several classifiers for uncertain data have been developed to tackle this uncertainty. However, the existing classifiers do not consider the dependencies among uncertain features, even though this dependency has a critical effect on classification accuracy. Therefore, we propose a new Bayesian classification model that considers the correlation among uncertain features. To handle the uncertainty of data, new multivariate kernel density estimators are developed to estimate the class conditional probability density function of categorical, continuous, and mixed uncertain data. Experimental results with simulated data and real-life data sets show that the proposed approach is better than the existing approaches for classification of uncertain data in terms of classification accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a knowledge-based Decision Support System (DSS) for classification, formulation and solution of multiple objective linear programming problems. The authors propose a generic taxonomy which is used to classify commonly encountered types of linear programming problems. Classification of the problem, vis-a-vis the proposed taxonomy, is based on the interaction with the user to determine the attributes which best describe the context or setting of the problem. A total of twenty-four problem types are included in the taxonomy. Following classification, a problem type-specific rule base is invoked to assist the user in constraint formulation. A product blending linear programming problem is used to demonstrate this component of the system since these types of problems typically include more varied constraints, including ratio as well as additive types, A second rule base is invoked for formulation of the multiple criteria objective function, model solution and sensitivity analysis. An initial goal prioritization scheme is obtained by use of the Analytical Hierarchy Process [17]; the optimal goal ordering is obtained by interaction with the user in the form of pairwise attribute value tradeoffs. The system developed is intended for use by the OR-naive user who is more familiar with the content of a problem than he/she is with the mathematical tools needed to formulate and solve such models. The system is a model management tool designed to interpret user inputs and translate those inputs into a solvable multiple objective LP. This interface alleviates the technical burdens of content specification and solution. The approach expands previous formulation tools, such as those based on natural language processing [8], to a broader range of problem types in a multiple criteria environment. The system was implemented on a personal computer using VP-Expert, BASIC and LINDO, and is demonstrated on a multiple objective blending problem. The ability of the approach to accurately classify LP problems was tested on thirty-six subjects. Results suggest that correct classification of problems was more likely to occur when the system was used. [ABSTRACT FROM AUTHOR]

Protein–protein interaction networks are mathematical constructs where every protein is represented as a node, with an edge signaling that two proteins interact. These constructs have enabled a series of graph theoretic computational methods in the analysis of how cell life works. Such methods have found diverse applications from helping create more reliable interaction data, to identifying new protein complexes and predict their functionalities, and investigating the minimum requirements for cell life through protein essentiality. Our goal with this survey is to provide an overview of the research in the area from a network analysis perspective. In this work, we provide a brief introduction to protein–protein interaction networks, followed by the methods that we currently have to obtain such interactions and the databases they can be found at. Then, we proceed to discuss the network properties of protein–protein interaction networks and how they can be exploited to identify protein complexes and functional modules, as well as help classify proteins as essential. We finish this survey with a full bibliography on work in protein–protein interactions that could be of interest to operations research and computational science academicians and practitioners. [ABSTRACT FROM AUTHOR]

Instead of using the same ensemble for all data instances, recent studies have focused on dynamic ensembles in which a new ensemble is chosen from a pool of classifiers for each new data instance. Classifiers agreement in the region where a new data instance resides in has been considered as a major factor in dynamic ensembles. We postulate that the classifiers chosen for a dynamic ensemble should behave similarly in the region in which the new instance resides, but differently outside of this area. In other words, we hypothesize that high local accuracy, combined with high diversity in other regions, is desirable. To verify the validity of this hypothesis we propose two approaches. The first approach focuses on finding the k-nearest data instances to the new instance, which then defines a neighborhood, and maximizes simultaneously local accuracy and distant diversity, based on data instances outside of the neighborhood. The second method makes use of an alternative definition of the neighborhood: all data instances are in the neighborhood. However, the importance of data instances for accuracy and diversity depends on the distance to the new instance. We demonstrate through several experiments that the distance-based diversity and accuracy outperform all benchmark methods. [ABSTRACT FROM AUTHOR]

In data envelopment analysis (DEA), the concept of efficiency is examined in either Farrell (DEA) or Pareto senses. In either of these senses, the efficiency status of a decision making unit (DMU) is classified as either weak or strong. It is well established that the strong DEA efficiency is both necessary and sufficient for achieving the Pareto efficiency. For the weak Pareto efficiency, however, the weak DEA efficiency is only sufficient, but not necessary in general. Therefore, a DEA-inefficient DMU can be either weakly Pareto efficient or Pareto inefficient. Motivated by this fact, we propose a new classification of DMUs in terms of both DEA and Pareto efficiencies. To make this classification, we first demonstrate that the Farrell efficiency is based on the notion of FGL dominance. Based on the concept of dominance, we then propose and substantiate an alternative single-stage method. Our method is computationally efficient since (1) it involves solving a unique single-stage model for each DMU, and (2) it accomplishes the classification of DMUs in both input and output orientations simultaneously. Finally, we present a numerical example to illustrate our proposed method. [ABSTRACT FROM AUTHOR]

Logical analysis of data (LAD) is a rule-based data mining algorithm using combinatorial optimization and boolean logic for binary classification. The goal is to construct a classification model consisting of logical patterns (rules) that capture structured information from observations. Among the four steps of LAD framework (binarization, feature selection, pattern generation, and model construction), pattern generation has been considered the most important step. Combinatorial enumeration approaches to generate all possible patterns were mostly studied in the literature; however, those approaches suffered from the computational complexity of pattern generation that grows exponentially with data (feature) size. To overcome the problem, recent studies proposed column generation-based approaches to improve the efficacy of building a LAD model with a maximum-margin objective. There was still a difficulty in solving subproblems efficiently to generate patterns. In this study, a new column generation framework is proposed, in which a new mixed-integer linear programming approach is developed to generate multiple patterns having maximum coverage in subproblems at each iteration. In addition to the maximum-margin objective, we propose an alternative objective (minimum-pattern) to solve the LAD problem as a minimum set covering problem. The proposed approaches are evaluated on the datasets from the University of California Irvine Machine Learning Repository. The computational experiments provide comparable performances compared with previous LAD and other well-known classification algorithms. [ABSTRACT FROM AUTHOR]

We introduce a novel modification to standard support vector machine (SVM) formulations based on a limited amount of penalty-free slack to reduce the influence of misclassified samples or outliers. We show that free slack relaxes support vectors and pushes them towards their respective classes, hence we use the name relaxed support vector machines (RSVM) for our method. We present theoretical properties of the RSVM formulation and develop its dual formulation for nonlinear classification via kernels. We show the connection between the dual RSVM and the dual of the standard SVM formulations. We provide error bounds for RSVM and show it to be stable, universally consistent and tighter than error bounds for standard SVM. We also introduce a linear programming version of RSVM, which we call RSVMLP. We apply RSVM and RSVMLP to synthetic data and benchmark binary classification problems, and compare our results with standard SVM classification results. We show that relaxed influential support vectors may lead to better classification results. We develop a two-phase method called RSVM for multiple instance classification (MIC) problems, where RSVM formulations are used as classifiers. We extend the two-phase method to the linear programming case and develop RSVMLP. We demonstrate the classification characteristics of RSVM and RSVMLP, and report our classification results compared to results obtained by other SVM-based MIC methods on public benchmark datasets. We show that both RSVM and RSVMLP are faster and produce more accurate classification results. [ABSTRACT FROM AUTHOR]

Kernel-based methods (KBMs) such as support vector machines (SVMs) are popular data mining tools for solving classification and regression problems. Due to their high prediction accuracy, KBMs have been successfully used in various fields. However, KBMs have three major drawbacks. First, it is not easy to obtain an explicit description of the discrimination (or regression) function in the original input space and to make a variable selection decision in the input space. Second, depending on the magnitude and numeric range of the given data points, the resulting kernel matrices may be ill-conditioned, with the possibility that the learning algorithms will suffer from numerical instability. Although data scaling can generally be applied to deal with this problem and related issues, it may not always be effective. Third, the selection of an appropriate kernel type and its parameters can be a complex undertaking, with the choice greatly affecting the performance of the resulting functions. To overcome these drawbacks, we present here the sparse signomial classification and regression (SSCR) model. SSCR seeks a sparse signomial function by solving a linear program to minimize the weighted sum of the ℓ-norm of the coefficient vector of the function and the ℓ-norm of violation (or loss) caused by the function. SSCR employs the signomial function in the original variables and can therefore explore the nonlinearity in the data. SSCR is also less sensitive to numerical values or numeric ranges of the given data and gives a sparse explicit description of the resulting function in the original input space, which will be useful for the interpretation purpose in terms of which original input variables and/or interaction terms are more meaningful than others. We also present column generation techniques to select important signomial terms in the classification and regression processes and explore a number of theoretical properties of the proposed formulation. Computational studies demonstrate that SSCR is at the very least competitive and can even perform better compared to other widely used learning methods for classification and regression. [ABSTRACT FROM AUTHOR]

We present a new column generation algorithm for the determination of a classifier in the two classes LAD (Logical Analysis of Data) model. Unlike existing algorithms who seek a classifier that at the same time maximizes the margin of correctly classified observations and minimizes the amount of violations of incorrectly classified observations, we fix the margin to a difficult-to-achieve target and minimize a piecewise convex linear function of the violation of incorrectly classified observations. Moreover a part of the training set, called control set, is reserved to select, among all feasible classifiers found by the algorithm, the one with highest performance on that set. One advantage of the proposed algorithm is that it essentially does not require any calibration. Computational results are presented that show the effectiveness of this approach. [ABSTRACT FROM AUTHOR]

We propose two extensions of the Logical Analysis of Data (LAD) methodology, designed in the context of diagnosing growth hormone deficiencies. On the one hand, combinatorial regression extends the standard methodology from classification problems to regression problems; it permits to predict the final height of children with particular growth troubles. On the other hand, function-based patterns extend the standard notion of pattern, leading to both accurate and simple models; it allows to produce an efficient diagnosis, straightforwardly usable by a general practitioner, that settles most of the doubtful cases of growth hormone deficiencies among short children. In both cases, we show the interest of the LAD extensions for each application, and we also point out the more general use that can be achieved through the two proposed approaches. [ABSTRACT FROM AUTHOR]

Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. We investigate properties of a mixed-integer programming based multi-category classification model that allows for the pre-specification of limits on inter-group misclassification rates. The mechanism by which the limits are satisfied is the use of a reserved judgment region, an artificial category into which observations are placed whose attributes do not sufficiently indicate membership to any particular group. The method is shown to be a consistent estimator of a classification rule with misclassification limits, and performance on simulated and real-world data is demonstrated. [ABSTRACT FROM AUTHOR]

We consider the linear classification method consisting of separating two sets of points in d-space by a hyperplane. We wish to determine the hyperplane which minimises the sum of distances from all misclassified points to the hyperplane. To this end two local descent methods are developed, one grid-based and one optimisation-theory based, and are embedded into a VNS metaheuristic scheme. Computational results show these approaches to be complementary, leading to a single hybrid VNS strategy which combines both approaches to exploit the strong points of each. Extensive computational tests show that the resulting method can always be expected to approach the global optimum close enough that any deviations from the global optimum are irrelevant with respect to the classification power. [ABSTRACT FROM AUTHOR]

The development of credit risk assessment models is often considered within a classification context. Recent studies on the development of classification models have shown that a combination of methods often provides improved classification results compared to a single-method approach. Within this context, this study explores the combination of different classification methods in developing efficient models for credit risk assessment. A variety of methods are considered in the combination, including machine learning approaches and statistical techniques. The results illustrate that combined models can outperform individual models for credit risk analysis. The analysis also covers important issues such as the impact of using different parameters for the combined models, the effect of attribute selection, as well as the effects of combining strong or weak models. [ABSTRACT FROM AUTHOR]

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. [ABSTRACT FROM AUTHOR]

The objective of this study was to distinguish within a population of patients with known or suspected coronary artery disease groups at high and at low mortality rates. The study was based on Cleveland Clinic Foundation's dataset of 9454 patients, of whom 312 died during an observation period of 9 years. The Logical Analysis of Data method was adapted to handle the disproportioned size of the two groups of patients, and the inseparable character of this dataset - characteristic to many medical problems. As a result of the study, we have identified a high-risk group of patients representing 1/5 of the population, with a mortality rate 4 times higher than the average, and including 3/4 of the patients who died. The low-risk group identified in the study, representing approximately 4/5 of the population, had a mortality rate 3 times lower than the average. A Prognostic Index derived from the LAD model is shown to have a 83.95% correlation with the mortality rate of patients. The classification given by the Prognostic Index was also shown to agree in 3 out of 4 cases with that of the Cox Score, widely used by cardiologists, and to outperform it slightly, but consistently. An example of a highly reliable risk stratification system using both indicators is provided. [ABSTRACT FROM AUTHOR]

The classification problem is to determine the class of an object when it is costly to observe the values of its attributes. This type of problem arises in fault diagnosis, in the design of interactive expert systems, in reliability analysis of coherent systems, in discriminant analysis of test data, and in many other applications. We introduce a generic decision rule that specifies the next attribute to test at any location in a decision tree. Random searches and tabu searches are applied to determine the best specific form of the rule. The most successful heuristics that we developed are based on the tabu search paradigm. We present computational results for problems with a variety of characteristics and compare our heuristics to an exact dynamic programming algorithm. [ABSTRACT FROM AUTHOR]

Research into the accuracy of mixed integer programming models for discrimination and classification, and the efficacy of heuristics developed for them, has been hampered by the inability to solve to optimality problems with moderate to large sample sizes. We present encouraging preliminary results for a decomposition approach that allows solution of models with dimensions previously considered prohibitive. [ABSTRACT FROM AUTHOR]